How to Simplify Variable Expressions

How to Simplify Variable Expressions

Learn the definition of variable and expression and how to simplify variable expressions.

Step by step guide to simplifying variable expressions

  • In algebra, a variable is a letter used to stand for a number. The most common letters are: \(x, y, z, a, b, c, m\) and \(n\).
  • An algebraic expression is an expression contains integers, variables, and math operations such as addition, subtraction, multiplication, division, etc.
  • In an expression, we can combine “like” terms. (values with same variable and same power)

Simplifying Variable Expressions – Example 1:

Simplify this expression. \(2 \ x \ + \ 3 \ x \ + \ 4=\)?

Solution:

Combine “like” terms. Then: \(2 \ x \ + \ 3 \ x \ = 5 \ x \) (remember you cannot combine variables and numbers).

Then: \(2 \ x \ + \ 3 \ x \ + \ 4=5 \ x \ + \ 4\) (remember you cannot combine variables and numbers).

Simplifying Variable Expressions – Example 2:

Simplify this expression. \(12 \ – \ 3 \ x^{2} \ + \ 5 \ x \ + \ 4 \ x^{2}=\)?

Solution:

Combine “like” terms. \(- \ 3 \ x^{2} \ + \ 4 \ x^{2}=x^{2}\)
Then: \(12 \ – \ 3 \ x^{2} \ + \ 5 \ x \ + \ 4 \ x^{2}\) \(=12 \ + \ x^2 \ + \ 5 \ x\). Write in standard form (biggest powers first): \(x^2 \ + \ 5 \ x \ + \ 12\)

Simplifying Variable Expressions – Example 3:

Simplify this expression. \((10x+2x+3)=\)?

Solution:

Combine “like” terms. Then: \((10x+2x+3)=12x+3\) (remember you cannot combine variables and numbers).

Simplifying Variable Expressions – Example 4:

Simplify this expression. \(12-3x^2+9x+5x^2=\)?

Solution:

Combine “like” terms: \(-3x^2+5x^2=2x^2\)
Then: \(12-3x^2+9x+5x^2=12+2x^2+9x\). Write in standard form (biggest powers first): \(2x^2+9x+12\)

Exercises for Simplifying Variable Expressions

Simplify each expression.

  • \(\color{blue}{– 2 – x^2 – 6x^2}\)
  • \(\color{blue}{ 3 + 10x^2 + 2}\)
  • \(\color{blue}{ 8x^2 + 6x + 7x^2}\)
  • \(\color{blue}{5x^2 – 12x^2 + 8x }\)
  • \(\color{blue}{– 2(4 – 6x) – 3x }\)
  • \(\color{blue}{ 9 – 2x + 5x + 2}\)

Download Simplifying Variable Expressions Worksheet

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Answers

  • \(\color{blue}{– 7x^2 – 2}\)
  • \(\color{blue}{10x^2 + 5}\)
  • \(\color{blue}{15x^2 + 6x}\)
  • \(\color{blue}{– 7x^2 + 8x}\)
  • \(\color{blue}{9x \ – 8 }\)
  • \(\color{blue}{3x \ + 11}\)

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